The light is being reflected inside the bulb.How to fix it?
To implement this, you just have to ensure that the light from the filament is not bouncing off or interacting with too many surfaces (in technical terms 'bounces').In our case, if the light from the filament comes through the front of the bulb, it means the emission ray from the filament is converted to transmission ray (at the front portion of bulb) and reaches camera. Which means 2 bounces. But in the case of the additional reflections, the bounces are more. 

So all we have to do is, make the rays which have more than 2 bounces invisible. We can get this bounce information from 'Ray depth' of 'Light path' node. 


  Ray Depth is the Number of times the ray has “bounced”, i.e. been reflected
  or transmitted on interaction with a surface.


In material node editor, Shift+A and Input>Light path. Also, we can get the 'greater than' operation from math node. Shift+A, Converter>Math and change the operation in the drop down menu to 'greater than'.

Check out the following node setup for emission material of the filament.You can do the same for the rest of the materials that are getting reflected.